Question

what's the difference between those methods of finding the average ,
for 8 numbers
98,77,86,92,80,70,94,65
method 1 :-
sumation/8
method 2 :-
98+77/2=87.5
87.5+86/2=86.75
.... and so on

avg1=82.75

avg2=75.3359..

Answer 1

Method one is correct. But if you do method 2:

\[ \frac{98+77}{2}=87.5\\
\, \\
\frac{87.5+86}{2}=86.75\\
...\]
Essentially what you are doing is this:
\[\Large \frac{\frac{\frac{98+77}{2}+86}{2}+92}{2}...\]

Answer 2

then it depand on the arrange of numbers and get diffrent answer each time right ?

Answer 3

Yeah

Answer 4

so what if i arrange them from the smallest ?

Answer 5

wont that be good approximation for the avg ?

Answer 6

You mean if you do:
\[\Large \frac{\frac{\frac{65+70}{2}+77}{2}+80}{2}...\] instead?

Answer 7

yeah

Answer 8

i would get 94.13 which is far away from avg .
hmm so which is better arrange them randomly ?

Answer 9

Well method 2 is simply an incorrect method of finding the mean.

Answer 10

naaa lol dnt say its wrong haha
im doing my senior project to convince ppl it culd be approximation method :P
its not wrong 100%

Answer 11

Well I suppose there are other ways to calculate the mean, like the geometric mean or the harmonic mean. I'm not familiar with this method of calculating it. And the fact that it gives different answers when you order the numbers differently doesn't seem terribly useful

Answer 12

But if you can do a proof for it, that's better than just giving examples.

Answer 13

ik :D
im just doing my jop
its worth if it give good approximation for n > 2000 or somthing

Answer 14

maybe. DId you prove that?

Answer 15

not yet

Answer 16

i think if the numbers were ordered and the difference between each 2 adjacent numbers remained the same then you could use method 2, right?

Answer 17

that would be complicated , but some how uve got a ponit i have to determine the Error range